To find the interquartile range (IQR), follow these steps:
- Order the data from least to greatest.
- Find the median of the entire data set. This splits the data into two halves.
- Find the lower quartile (Q1) , which is the median of the lower half of the data (the 25th percentile).
- Find the upper quartile (Q3) , which is the median of the upper half of the data (the 75th percentile).
- Calculate the interquartile range by subtracting the lower quartile from the upper quartile:
IQR=Q3−Q1\text{IQR}=Q3-Q1IQR=Q3−Q1
The IQR represents the range of the middle 50% of the data, showing the spread of the central portion of the dataset
. For example, if Q1 is 3 and Q3 is 12, then the IQR is 12−3=912-3=912−3=9
. This method helps to measure variability while reducing the effect of outliers compared to the full range
